Effective interface conditions for a porous medium type problem
CIAVOLELLA, Giorgia
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
DAVID, Noemi
Université de Lyon
Institut Camille Jordan [ICJ]
Modélisation mathématique, calcul scientifique [MMCS]
Université de Lyon
Institut Camille Jordan [ICJ]
Modélisation mathématique, calcul scientifique [MMCS]
POULAIN, Alexandre
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Sorbonne Université [SU]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Modelling and Analysis for Medical and Biological Applications [MAMBA]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Sorbonne Université [SU]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Modelling and Analysis for Medical and Biological Applications [MAMBA]
CIAVOLELLA, Giorgia
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation Mathématique pour l'Oncologie [MONC]
Institut de Mathématiques de Bordeaux [IMB]
DAVID, Noemi
Université de Lyon
Institut Camille Jordan [ICJ]
Modélisation mathématique, calcul scientifique [MMCS]
Université de Lyon
Institut Camille Jordan [ICJ]
Modélisation mathématique, calcul scientifique [MMCS]
POULAIN, Alexandre
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Sorbonne Université [SU]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Modelling and Analysis for Medical and Biological Applications [MAMBA]
< Réduire
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Sorbonne Université [SU]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Modelling and Analysis for Medical and Biological Applications [MAMBA]
Langue
en
Article de revue
Ce document a été publié dans
Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications. 2024-02-06
European Mathematical Society
Résumé en anglais
Motivated by biological applications on tumour invasion through thin membranes, we study a porous-medium type equation where the density of the cell population evolves under Darcy's law, assuming continuity of both the ...Lire la suite >
Motivated by biological applications on tumour invasion through thin membranes, we study a porous-medium type equation where the density of the cell population evolves under Darcy's law, assuming continuity of both the density and flux velocity on the thin membrane which separates two domains. The drastically different scales and mobility rates between the membrane and the adjacent tissues lead to consider the limit as the thickness of the membrane approaches zero. We are interested in recovering the <i>effective interface problem</i>and the transmission conditions on the limiting zero-thickness surface, formally derived by Chaplain et al., (2019), which are compatible with nonlinear generalized Kedem-Katchalsky ones. Our analysis relies on <i>a priori<i> estimates and compactness arguments as well as on the construction of a suitable extension operator which allows to deal with the degeneracy of the mobility rate in the membrane, as its thickness tends to zero.< Réduire
Mots clés en anglais
Membrane boundary conditions
Effective interface
Porous medium equation
Nonlinear reaction-diffusion equations
Tumour growth models
Projet Européen
Asymptotic approach to spatial and dynamical organizations
International Doctoral Training in Mathematical Sciences in Paris
International Doctoral Training in Mathematical Sciences in Paris
Origine
Importé de halUnités de recherche